Open AccessTHE INVESTIGATION OF PARTICLE MOVEMENT ON A HELICAL SURFACE UNDER THE EFFECT OF THE FORCE OF ITS WEIGHT
Author(s) -
Tatiana Volina
Publication year - 2020
Publication title -
prikladnaâ geometriâ i inženernaâ grafika
Language(s) - English
Resource type - Journals
ISSN - 0131-579X
DOI - 10.32347/0131-579x.2020.99.65-78
Subject(s) - helicoid , surface (topology) , plane (geometry) , geometry , spiral (railway) , particle (ecology) , line (geometry) , inclined plane , cross section (physics) , physics , ruled surface , mechanics , screw axis , classical mechanics , mathematics , optics , mathematical analysis , geology , oceanography , quantum mechanics
Differential equations of particle movement on the rough surface of the spiral gutter under the effect of the force of own weight are obtained in the article. The curve of the cross section of the gutter with a vertical plane passing through the axis of the surface is given by parametrical equations in general form. Special cases for individual cross-sectional lines (a straight line and a circle) are considered. If the section is an arc of a circle, a spiral gutter is formed. In the particular case when the cross section is a straight line inclined to the axis upwards, then the helical surface is an oblique helicoid. The equations are solved by numerical methods and trajectories of a particle movement along a helical surface are constructed. After the motion stabilizes, the particle has a constant speed and its trajectory is a helical curve. For this particular case, analytical dependencies that allow calculating the speed of a particle and its distance from the axis of the surface were found. The case, when an angle of elevation of the lowest helical curve of the gutter is equal to the angle of friction of the particle on the surface, is also considered. In the case of a spiral gutter, the elevation angle of its lower helical line should be greater than the friction angle in order to avoid congestions during transportation of particles of the technological material.